Having the eigenvalue of my matrix (Hamiltonian), how can I get the eigenvector associated with it?

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Auryn_ 2017-6-13

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评论： Auryn_ 2017-6-13

Hello, I have a given eigenvalue (energy) of my matrix (Hamiltonian), which is known. Now I want to obtain the eigenvector associated with it? Is there any function similar to eig to do so? Thanks in advance.

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Answer 1

Matt J 2017-6-13

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V=null(A-eigenvalue*eye(size(A))

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John D'Errico 2017-6-13

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A virtue of this solution is that if the eigenvalue has multiplicity greater than 1, then V will contain all the eigenvectors associated with that eigenvalue.

A = ones(3);

A has one eigenvalue of 3, but 0 is an eigenvalue, with multiplicity 2.

null(A-3*eye(size(A)))
ans =
     -0.57735
     -0.57735
     -0.57735
null(A-0*eye(size(A)))
ans =
            0       0.8165
     -0.70711     -0.40825
      0.70711     -0.40825